Abstract: The problems of stability and control for nonlinear time-delay systems represented by a Takagi-Sugeno（T-S） fuzzy model are investigated. Firstly, less conservative delay-dependent stability criterion in terms of Linear Matrix Inequalities（LMIs） is obtained by choosing a recently developed free-matrix-based integral inequality. Secondly, combined with Finsler lemma, a flexible fuzzy state feedback controller design method is presented under the imperfect premise matching strategy. The design method does not require the fuzzy controller to share the same premise membership functions and the same number of fuzzy rules as the fuzzy model. Finally, two numerical examples are given to show the progressiveness and effectiveness of the presented theories.

Key words: Takagi-Sugeno（T-S） fuzzy model, nonlinear time-delay systems, free-matrix-based integral inequality, imperfect premise matching, Finsler lemma

摘要： 研究了基于Takagi-Sugeno（T-S）模糊模型描述的非线性时滞系统的稳定性与控制问题。选择一个最近提出的基于自由权矩阵的积分不等式，以线性矩阵不等式（LMIs）形式给出了保守性较小的时滞依赖的稳定性准则。基于前提不匹配策略，结合Finsler引理，提出了更为灵活的模糊状态反馈控制器的设计方法，该方法不要求控制器和系统分享共同的前提隶属函数和规则数目。最后，给出两个仿真算例，证明了所提理论的先进性和有效性。

关键词: Takagi-Sugeno（T-S）模糊模型, 非线性时滞系统, 基于自由权矩阵的积分不等式, 前提不匹配, Finsler引理